In this section we briefly introduce the basic notions and results on both Morse–Bott theory and Lie groupoids which will be used throughout this paper. Much of the classical results about Morse theory may be found for instance in [1]}, [2]}, [3]}, [4]}, [5]}. For the general notions regarding Lie groupoids, Morita equivalences and Riemannian groupoids we follow [6]}, [7]}, [8]} closely.
